I assume you're in the US. In the UK you can get an ultrasonic device that's supposed to keep mice at bay. Frankly, though, you have no alternative but to poison. However, contrary to previous advice it will kill cats and dogs.
Another, less reliable remedy would several traps. You'd need a lot. You can get ones that imprison rather than kill and you can release them well away from your farm. Use chocolate to attract them, they love it. Stragely enough, they don't like cheese that much!!